Problem: Evaluate $\int4\,\sec4x\,\tan4x\,dx\,$. Choose 1 answer: Choose 1 answer: (Choice A) A $\sec4x+C$ (Choice B) B $\sec x+C$ (Choice C) C $4\tan4x+C$ (Choice D) D $\tan4x+C$
Explanation: We use a $u$ -substitution. Let $u=4x$ so that $du=4\,dx\,$. Then $\begin{aligned} &\phantom{=}\int4\,\sec4x\,\tan4x\,dx \\\\ &=\int\sec u\,\tan u \,du \\\\ &=\sec u+C= \sec4x+C \end{aligned}$